Investigate alternative to CellValues

[termi-official]

It is interesting to explore alternative evaluation modes to CellValues. Resizing arrays is cheap and in most cases non-allocating, so we can easily call it once per cell.

julia> @btime resize!($A,5)
  4.160 ns (0 allocations: 0 bytes)
5-element Vector{Float64}:
 -9.112500000000002e-5
  0.00011137500000000004
 -0.00013612500000000004
  0.00011137500000000004
  0.00011137500000000004

julia> @btime resize!($A,5)
  3.810 ns (0 allocations: 0 bytes)
5-element Vector{Float64}:
 -9.112500000000002e-5
  0.00011137500000000004
 -0.00013612500000000004
  0.00011137500000000004
  0.00011137500000000004

Furthermore the evaluation of ansatz functions per quadrature point is also not that bad.

julia> ip = Lagrange{RefHexahedron,2}()
Lagrange{RefHexahedron, 2}()

julia> @btime Ferrite.shape_values!($A, $ip, Vec((0.1,0.1,0.1)))
  142.555 ns (0 allocations: 0 bytes)

julia> B = zeros(Vec{3}, 27)
27-element Vector{Vec{3, Float64}}:
 [0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0]
 [0.0, 0.0, 0.0]

julia> @btime Ferrite.shape_gradients_and_values!($B, $A, $ip, Vec((0.1,0.1,0.1)))
  451.777 ns (0 allocations: 0 bytes)

and there is room for optimization

julia> function shape_values(A, ip::Lagrange{RefHexahedron, 1}, ξ::Vec{3})
           ξ_x = ξ[1]
           ξ_y = ξ[2]
           ξ_z = ξ[3]
           Nx = ((1 - ξ_x), (1 + ξ_x))
           Ny = ((1 - ξ_y), (1 + ξ_y))
           Nz = ((1 - ξ_z), (1 + ξ_z))
           A[1] = Nx[1] * Ny[1] * Nz[1] / 8
           A[2] = Nx[2] * Ny[1] * Nz[1] / 8
           A[3] = Nx[2] * Ny[2] * Nz[1] / 8
           A[4] = Nx[1] * Ny[2] * Nz[1] / 8
           A[5] = Nx[1] * Ny[1] * Nz[2] / 8
           A[6] = Nx[2] * Ny[1] * Nz[2] / 8
           A[7] = Nx[2] * Ny[2] * Nz[2] / 8
           A[8] = Nx[1] * Ny[2] * Nz[2] / 8
       end
shape_values (generic function with 2 methods)

julia> @btime Ferrite.shape_values!($A, $ip, Vec((0.1,0.1,0.1)))
  39.889 ns (0 allocations: 0 bytes)

julia> @btime shape_values($A, $ip, Vec((0.1,0.1,0.1)))
  6.930 ns (0 allocations: 0 bytes)